A cone has a volume of 98 cm³ - Edexcel - GCSE Maths - Question 15 - 2017 - Paper 1

To find the height of the cone, we can use the formula for the volume of a cone:

$V = \frac{1}{3} \pi r^2 h$

Given:

• Volume, $V = 98$ cm³
• Radius, $r = 5.13$ cm

1. Substitute the values into the formula: $98 = \frac{1}{3} \pi (5.13)^2 h$

2. Calculate $(5.13)^2$: $(5.13)^2 \approx 26.3769$

3. Substitute this back into the equation: $98 = \frac{1}{3} \pi (26.3769) h$

4. Multiply both sides by 3 to eliminate the fraction: $294 \approx \pi (26.3769) h$

5. Divide both sides by $\, \pi (26.3769) \,$ to isolate $h$: $h \approx \frac{294}{\pi (26.3769)}$

6. Calculate the approximate value using $\, \pi \approx 3.14$: $h \approx \frac{294}{3.14 \times 26.3769} \approx \frac{294}{82.7079} \approx 3.56\ cm$

Thus, the estimated height of the cone is approximately 3.56 cm.